System for computing electric power flow

ABSTRACT

Disclosed herein is a simulated power system including a network of resistances, power sources, and loads corresponding respectively to line reactances, generators, and loads of an actual power system, and further including measuring devices for determining voltages and current flow between selected nodes (e.g. m and n) of the network, wherein the active power Pmn and the reactive power Qmn through the branch between the nodes can be calculated rapidly according to the formulas   WHERE theta M AND theta N ARE THE PHASE ANGLES AT THE RESPECTIVE NODES AND ARE PROPORTIONAL TO THE VOLTAGES AT THE NODES, AND Delta Vm and Delta Vn are difference voltages between actual and standard voltages at the selected nodes. In the simulated system the power sources are provided by constant current supply devices or constant voltage devices, and the load units are provided by constant current withdrawal devices, wherein the power sources and loads are connected to predetermined nodes of the network.

United States Patent Mitsui et al.

[4 1 July 4, 1972 [54] SYSTEM FOR COMPUTING ELECTRIC POWER FLOW [72]Inventors: Tsuneo Mitsui, .Tokyo; Jun-[chi Baba,

Kobe; Ikuo Yamada, Kobe, all of Japan [73] Assignees: Tokyo DenryokuKabushiki Kaisha; Mitsubishi Denki Kabushiki Kaisha, Tokyo, Japan [22]Filed: June 23,1970

[21] Appl.No.: 49,122

[52] U.S.Cl ..235/185,235/l5l.2l,235/l84 [51] Int. Cl. ..G06g 7/50 [58]Field of Search ..235/184, 185,151.21; 324/57 F? [56] References CitedUNITED STATES PATENTS 2,323,588 7/1943 Enns ..235/185 2,49 I ,09512/1949 Enns...... ....235/l85 2,301,470 11/1942 Starr ..235/l85 PrimaryExaminer-Felix D. Gruber A!t0rneyR0bert E. Burns and Emmanuel .l. Lobato1 1 ABSTRACT Disclosed herein is a simulated power system including anetwork of resistances, power sources, and loads correspondingrespectively to line reactances, generators, and loads of an actualpower system, and further including measuring devices for determiningvoltages and current flow between selected nodes (e.g. m and n) of thenetwork, wherein the active power Pmn and the reactive power Qmn throughthe branch between the nodes can be calculated rapidly according to theformulas where 0m and Br: are the phase angles at the respective nodesand are proportional to the voltages at the nodes, and AVm and AVn aredifference voltages between actual and standard voltages at the selectednodes. In the simulated system the power sources are provided byconstant current supply devices or constant voltage devices, and theload units are provided by constant current withdrawal devices, whereinthe power sources and loads are connected to predetermined nodes of thenetwork.

4 Claims, 5 Drawing Figures BACKGROUND OF THE INVENTION This inventionrelates to a simulated electric power system for use in rapidlycomputing a power flow through an actual electric power system.

The power flow computing system of this invention can be employed tocompute active, reactive powers and voltages, and phase angles of theelectric power system, within a short interval of time during the normaloperation thereof, and also during system disturbances resulting frompredetermined suspension of the associated power equipments, or fromoccurrence of any failure etc. for the purpose of safely operating theelectric power system in accordance with the result of the particularcomputation.

In the past, alternating current network analyzers have been used tocompute power flow through an electric power system. Upon computing apower flow through a particular large-scaled, complicated electric powersystem, the conventional type of alternating current network analyzershave exhibited the following disadvantages:

1. Such network analyzers have been subject to a limitation as to thenumber of electric generators included in the electric power system sothat they can not satisfactorily cover the electric power system. If itis attempted to satisfactorily cover the electric power system by theparticular alternating current network analyzer then the latter isrequired to be greatly increased in its number ofelements; and

2. The larger and more complicated the electric power system is the moredifficult it will be to control the parameters involved. This makes itimpossible to effect a stable computation.

Recently digital computers have been used to compute the power flow inlarge-scaled and complicated systems, and it has been required to changethe large simulated system thereof, for example, upon system switching.Also upon changing the output from a particular generator it has beenrequired to repeat the computation so as to cause the result of thatcomputation to converge.

SUMMARY OF THE INVENTION Accordingly, it is an object of the inventionto provide a new and improved system for computing a power flow throughan electric power system in a rapid and simple manner through theutilization of a simple network simulating the electric system.

The invention accomplishes this object by providing the simulated systemin the form of a resistance network substantially simulating theelectric power system, and including a plurality of simulated branchlines interconnected at the nodes thereof; generator units simulatingeach of the generators disposed in the electric power system andconnected to each of selected ones of the nodes; and load unitssimulating each of the loads disposed in the electric power system andconnected to each of selected ones of the nodes; means for measuringvoltages at the nodes and currents flowing through the simulated branchlines; means for computing the actual active and reactive powers fromthe measured currents; and means for computing the actual voltages andphase angles thereof from the measured voltages.

Preferably, the simulated generator unit may comprise threepotentiometers for setting the active and reactive powers and voltagerespectively, and an operational amplifier selectively connectable tothe potentiometers. For the active and reactive power simulation, theoperational amplifier has a feedback resistor connected across the inputand output thereof and includes means for taking the output from theunit through the feedback resistor to provide a source of constantcurrent. For the voltage simulation the operational amplifier provides asource of constant voltage.

Similarly the simulated load unit may comprise a pair of potentiometersfor setting the resistance and reactance of the actual load, anoperational amplifier having a feedback resistor connected across theinput and output thereof and selectively connectable to thepotentiometers, and means for taking the output from the unit throughthe feedback resistor to provide a source of constant current.

BRIEF DESCRIPTION OF THE DRAWINGS The invention will become more readilyapparent from the following detailed description taken in conjunctionwith the accompanying drawings in which:

FIG. 1a is a schematic circuit diagram of one branch line of an electricpower system to which the invention is applicable;

FIG. 1b is an equivalent resistance network useful in explaining theprinciples of the invention;

FIG. 2 is a circuit diagram of a simulated generator unit constructed inaccordance with the principles of the inventlon;

FIG. 3 is a circuit diagram of a simulated load unit constructed inaccordance with the principles of the invention;

FIG. 4 is a circuit diagram of a simulated resistance network used ineffecting the computation of the reactive power and voltage inaccordance with the principles of the invention; and

FIG. 5 is a circuit diagram of a simulated resistance network used inefiecting the computation of the active power and relative phase angleof voltage in accordance with the princi ples of the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT Since actual electric powersystems are very complicated in configuration, the power flowcharacteristics thereof are also complicated. However suchcharacteristics can be estimated from the power flow characteristic of asystem branch such as shown in FIG. 1a or b of the drawings. Referringnow to FIGS. la and b, a connection point or a node m is connected toanother node n through an impedance Z,,,, (FIG. la) or an equivalentresistance r (FIG. 1b). It is now assumed that the voltages at nodes mand n are expressed, in vector form, as V e and V e respectively, andthe impedance has flowing therethrough a power of P j Q,,,,, where ebase of Napierian logarithm j unit of imaginary number equal to F1- P,active power 0,, reactive power, and

a,,,,, arctan (Rmn/Xmn) Under the assumed condition, the followingequation is held:

un: Qmn m 1101 (I) where I,,,,,* conjugate value of complex current,I,,,,, flowing between the nodes in and n. The variables Vm, Vn, Zmn,Pm, Qm, etc., are based on a per-unit system in all equations of thisdisclosure. In the above equation (1) a bagging reactive power isconsidered to be positive. Substituting 1* V V,,)*/Z,,,,,, where (V,,.V,,)* and Z,,,,,* are conjugate values of the complex values V,, V,,)and 2 into the equation (1) gives mn uin in (VIII nr mn By using thetrigonometric functions, the equation becomes P +jQ,,.,. M cos a sin(6,,, 6

sin am" cos (6," (9,1)]

+ j cos a cos (6,,. 60}

%l' sin a,,,,. sin (6, GU]

Thus the active and reactive powers mn and Q,,,,, respectively can beexpressed by the following equation:

sin a sin (0, 0,,) (4) For purposes of simplicity it is assumed that (1)the active power P is determined only by a phase difference between thevoltage V and V, at the nodes m and n, and that (2) the reactive powerQ,,,,, is determined only by a difference in voltage between the nodes mand n. Then we have sin( 6, 6,) E 0,, (because 0,,,0,, is small),

mn E mrl mn III" (because m" 2 cos a, E 1.0, and l cos(0,,, 0 aw, 0Further it is assumed that the voltages V,,, and V, are slightlydifferent from a reference voltage of l per unit and can be expressed byl AV and l AV, respectively. Then the equations (3) and (4) reducerespectively to:

A lll um I 5 m m n) If the active power P,,,,, is computed in accordancewith the first term of the equation, (5) the same can be expressed by m"m )l nm on the assumptions that the voltages V, and V respectively atboth nodes m and n are approximately equal to each other V, E V therelationship V, E 1.0 per unit is held, and that the resistance R,,,,,is negligibly small. The third and the 4th term of equation (6)correspond to the reactive power consumed by the current flowing throughthe reactance of transmission lines.

The reactive power Q can be expressed by the quation Qmn==(AVmAVn)/Xmn,(8) because the resistance Rmn is negligibly small, and the reactivepower consumed by the current flowing through the reactances oftransmission lines is compensated by the reactive power supplied by acharging current of a capacitance between transmission lines to ground.(It is generally referred to as surge impedance loading.)

But in case of a heavily loaded long distance transmission line, it isnecessary to have a suitable compensation circuit in the simulatedsystem of the invention in order to improve the accuracy. That is: (l)the active power Pmn is approximately determined only by the phasedifference between the voltage Vm and Vn at the nodes m and n; and, (2)the reactive power Qmn is determined only by the voltage differencebetween the nodes m and n.-

On the other hand, a current i,,,, flowing from the modem to the node nas shown in FIG. lb follows Ohms Law and is given by the equation mn md/ m where v, voltage at the node m v,, voltage at the node n r,,,,,equivalent resistance simulating the actual line reactance between thenodes m and n.

By comparing the equations (7) and (9) it will be appreciated thatbetween the impedance network of FIG. 1(a) and the equivalent resistancenetwork of FIG. 1b, a correspondence is present between the active powerP,,.,. to the current i,,,, in the equivalent resistance network, andthe phase angle of the voltage 0,,, or 0,, to the voltage v,, or v, inthe equivalent resistance network. Then, by comparing equations (8) and(9), a correspondence is seen between the relative deviation Av or AV,of the voltage from the reference to the voltage v,,, or V,, for theresistance network, and the reactance X,,,,, to the resistance r,,,,, ofthe resistance network. It is noted that said calculation for theequivalent resistance network may be accomplished with respect to eitheralternating or direct current.

As a result, the power flow through the branch line of the electricpower system such as shown in FIG. 1(a) can be computed on thebasis ofthe parameters of the resistance network as shown in FIG. l(b) by takinginto account the correspondence of the parameters just described. Inthis regard, it is to be noted that all the parameters P Q,,,,,, 0, 0,,,AV,, and AV can not be simultaneously computed, but that the powerP,,,,, and the phase angles 0, and 6,, can be simultaneously computedwhile the power Q and the voltage deviations AV,

' and AV can be simultaneously computed using a resistance network.

Referring now to FIG. 2, there is illustrated a simulated generator unitconstructed in accordance with the principles of the invention. Thearrangement illustrated comprises a source of direct current powerrepresented by a pair of negative and positive terminals 10 and 12respectively, and three potentiometers 14P, Q and V, each having one endconnected to the terminal 10. The potentiometer 14? has its other endconnected to ground and has a slidable p serving to set an active powerlevel P; the potentiometer 14Q has its other end connected to theterminal 12 and has a slidable tap q serving to set a reactive powerlevel Q; and the potentiometer 14V has its other end connected to theterminal 12 and has a slidable tap v serving to set a voltage level v.Both the potentiometers and V also have fixed taps at their respectivecentral point connected to ground.

As shown in FIG. 2, a transfer relay generally designated by thereference numeral 16 includes an operating winding l6w, a movablecontact 16a and a pair of stationary contacts 16b and c, with thestationary contact 1612 connected to the slidable tap p on theactive-power potentiometer 14F, and with the movable contact 16anormally in engagement with the stationary contact 16b. The transferrelay 16 is operative to change the setting and computing of theparameter P to the setting and computing of the parameters Q and V andvice versa. The stationary contact 16c is'connected to a movable contact18a of a transfer switch generally designated by the reference numeral18 and including a pair of stationary contacts 18b and 0 connected tothe slidable taps q and v on the potentiometers MO and V respectively.The movable contact is normally in engagement with the stationarycontact 1812.

The transfer switch 18 interlocks with a switch 20 adapted to be openwhen the switch contact 180 is in engagement with the contact 1812, andto be closed when the movable contact 18a is put in engagement with thecontact 18c. The switch 18 is connected through a protective relay 22 toa control relay 24 for the purpose as will be apparent hereinafter. Thatis, the switch 20 includes contacts connected through two sets ofnormally open contacts 22a of the protective relay 22 across anoperating winding 24w of the control relay 24 including a set ofnormally closed contacts 24a, and also across a source of direct currentE The relay 22 includes an operating winding 22w connected across a pairof control terminals 26 as does the operating relay winding 16w. Theterminals 26 serve to apply a control signal to both the operatingwinding 16w and 22w upon setting and computing the parameters Q and V.

An operational amplifier 28 has one input connected to the movable relaycontact 16a and the other input connected to the set of normally closedcontacts 24a of the control relay 24 to serve as an adder. Then theoutput of the operational amplifier 28 is connected through resistor 30to a terminal 32 providing an output terminal of the simulated generatorunit.

The source E is adapted to energize a second transfer relay generallydesignated by the reference numeral 34. The transfer relay 34 includes amovable contact 34a connected to the junction of the resistor 30 and theoutput tenninal 32, and a pair of stationary contacts 34b and c. Themovable contact 34a is normally in engagement with the stationarycontact 34b which is, in turn, connected to an inverter 36 connected tothe set of control contacts 240, while the contact 340 is connected tothe junction of the operational amplifier 28 and the resistor 30.

In the arrangement illustrated it is noted that during the setting of Pof the generators and loads, and during the computing of the parametersP of line flow and 0, the relays 16 and 22 have no control signalapplied thereto through the control terminals 26, so that they are in adeenergized state; and, due to the interlocking of the switch 18 withthe switch 20, the relays 34 and 24 are in their deenergized stateexcept when the movable switch contact 180 is put in engagement with thestationary contact 180 to set a voltage. As a result, when the relay 16and the switch 18 are in their positions as illustrated in F IG. 2,wherein the contacts 16a and 18a are in engagement with the contacts 16band 18b respectively, a constant current circuit is formed of a closedloop consisting of the operational amplifier 28, the resistor 30, thecontact 34a engaging the contact 34b of the transfer relay 34, theinverter 36 and the normally closed control contacts 24a as will beapparent hereinafter. The engagement of the transfer contact 16a withthe contact 16b causes the arrangement of FIG. 2 to be ready for settingan active power or for computing the parameters P and 0, while theengagement of the transfer contact 18a with the contact 18b causes thearrangement to be ready for setting or computing the parameters Q and V.

The purpose of the protective relay 22 is to prevent the constantcurrent circuit as above described from being broken upon setting anactive power due to the energization of the relays 34 and 24. Suchenergization of the relays 34 and 24 may occur through the engagement ofthe transfer contact 18a with the contact 18c, and therefore the closingof the switch 20 when the transfer contact 16a is in engagement with thecontact 16b, to set an active power. I

The arrangement as above described is operated as follows: It is assumedthat an active power P is to be set. With the components maintained intheir positions illustrated, the slidable tap p on the P potentiometer14? is adjusted to provide a voltage of -V,, thereat corresponding tothe particular active power P. The voltage of V, is then applied throughthe contact 16b and a of the transfer switch 16 to the operationalamplifier 28. Under these circumstances it is assumed that theoperational amplifier 28 provides an output voltage of V which, in turn,appears at the output terminal 32 as a voltage V with an output currentof I flowinG through the resistor 30 and the output terminal 32 into aresistance network as will be described hereinafter in conjunction withFIG. 4 or 5.

' Under the assumed condition, the voltage of V is applied through thetransfer relay contact 34a and b, the inverter 36, and the closedcontrol contacts 24a to the other input to the operational amplifier 28serving also as an inverter. Thus the voltage V from the operationalamplifier 28 is expressed by the equation V V V Assuming that theresistor 30 has a magnitude of resistance of R the current I flowingthrough the resistor 30 is expressed by the equation 2" a)/ o-Substituting the equation (10) into the equation (11), gives theequation From the equation (12) it is seen that with the resistance R,remaining unchanged, the simulated generator unit provides the outputcurrent I determined only by the setting of the P potentiometer 14P.That is, the output current I is determined in accordance with thevoltage V set on the P potentiometer 14F and is independent of thevoltage V at the output terminal 32. Therefore the constant currentcharacteristic has been provided.

From the foregoing description it will be appreciated that if the Ppotentiometer 14 has its slidable tap p set to provide a voltage of Vcorresponding to the particular active power P, the simulated generatorunit of FIG. 2 can produce a simulated active power having theprescribed magnitude of P.

If it is desired to set a reactive power Q, the relays l6 and 22 can beenergized through the control terminal 26 to engage the transfer contact16a with the associated contacts 16c. The energization of the relay 22causes its contacts 22a to be closed which does not directly affect thenetwork because the transfer contact 18a remains in engagement with thecontact 18b. Then the slidable tap q on the potentiometer 140 issimilarly adjusted to provide a voltage corresponding to the particularreactive power Q. Thereafter the process as above described in terms ofthe active power will be repeated to permit the generation of simulatedreactive power having the prescribed magnitude of Q. It will beappreciated that the operational amplifier 28 also provides a source ofconstant current.

If it is desired to provide a particular voltage of V by the arrangementof FIG. 2, then the switch 18 is manually operated such that thetransfer contact is moved from the contact 18b to the contact 18c whichis accompanied by the closure of the normally open contacts of theswitch 20. Also, a control signal is applied to energize the transferrelays 16 and 22 through the control terminal 26. Therefore, thetransfer contact 16a engages the contact 18c and the protective contacts220 are closed to permit the relays 34 and 24 to be energized. Whenenergized, the relay 24 opens the contacts 240 to disconnect theinverter 36 from the operational amplifier 28. Also the relay 34 movesthe transfer contact 340 from the contact 34b to the contact 34c toshortcircuit the resistor 30.

Under these circumstances, the particular voltage of V set by thepotentiometer 14V is applied through the contacts 18c and a, and thecontacts 160 and a to the operational amplifier 28. Since theoperational amplifier 28 has no input applied from the inverter 36 andsince the resistor 30 is shortcircuited, an output voltage is providedidentical to the set voltage of V. If the operational amplifier 28 has alow output impedance, the same can be operated as a source of constantvoltage for providing a simulated voltage having the prescribedmagnitude of V.

Since an active power P from any generator is necessarily positive, theP potentiometer 14? is arranged for application of a negative voltage,and the reactive power Q may lead or lag in phase with respect to theassociated voltage so that the Q potentiometer 14Q includes theintermediate point connected to ground to permit a voltage set therebyto become either positive or negative. Similarly the potentiometer 14Vincludes the intermediate point connected to ground to set a deviationof a voltage from a reference voltage but not its absolute magnitudethereon. Thus the potentiometer 14V can provide either of simulatedpositive and negative voltages as the case may be.

Referring now to FIG. 3, there is illustrated a load network simulatingthe actual load in accordance with the principles of the invention. Thearrangement illustrated includes only the P potentiometer 14? forsetting a simulated resistance portion of the actual load, the Qpotentiometer 14P for setting a simulated reactance portion thereof, thetransfer 18, the operational amplifier 28, the resistor 30, the inverter36 and the terminals 10, 12 and 32 connected in the similar manner asabove described in conjunction with FIG. 2. Therefore the components aredesignated by the same reference numerals denoting the correspondingcomponents of FIG. 2 with the sufiix L. For example, the P potentiometeris designated that 14PL and the operational amplifier is designated at28L.

Since any load consumes an active power, the same can be considered toprovide a negative output. For this reason the P potentiometer 14PL isarranged to be applied with a positive voltage. On the other hand the Qpotentiometer 14QL for setting a simulated reactance portion of a loadmay have applied thereto a positive or a negative voltage for the samereasons as above described in conjunction with FIG. 2. In otherrespects, the arrangement is identical to that shown in FIG. 2.

Referring now to FIGS. 4 and 5, there are illustrated two specificresistance networks which form the basis for a computation of powerflow. FIG. 4 illustrates the case .wherein a reactive power Q and avoltage V are computed, while FIG. 5 illustrates the case wherein anactive power and a phase angle of a voltage are computed. In both theFigures like references numerals designate the corresponding oridentical components; In FIG. 4, each of the branch lines comprises apair of circuit breakers 40 and a resistor 42 whose resistance issubstantially equal in magnitude to the line reactance of thecorresponding branch line of the electric power system to be simulated.Furthermore, at least one node has connected thereto a simulated powergenerator unit 44 or 46 such as shown in FIG. 2 or a simulated load unit48 such as shown in FIG. 3, and one node chosen as a reference point isconnected to ground. For example, the node labelled V,,, has threebranch lines and the load unit 48 connected thereto while the nodeslabelled V,, and V have two branch lines and constant voltage generatorunits 44 connected thereto with the circuit breakers 40, resistors 42and breakers 40 connected in series circuit relationship in the namedorder between the nodes V,,

and V,, or V,. Thus, in FIG. 4, the generator units 44 are to prescribethe particular voltage V, and the generator unit 46 and load unit 48 toprescribe the particular reactive power Q.

The resistance network of FIG. is identical in configuration to thatshown in FIG. 4 excepting that the generator units 44 and shown in FIG.4 are replaced by constant current sources 45 for prescribing theparticular active power P, and that a selected one of the nodes isconnected to ground. For example, the node labelled 0, is connected toground to provide a reference point with respect to which a phase angleof each branch line is determined.

In the arrangement shown in either of FIGS. 4 and 5, the generator andload units are preset to provide a prescribed positive or negativeoutput, and the circuit breakers are suitably closed or opened tosimulate the particular electric power system to be computed. Then asuitable voltage is applied to the resistance network to cause currentsto flow therethrough. The voltages and currents for the respectivebranch lines are determined in accordance with Ohms and Kirchhofis laws.Under these circumstances the currents flowing through the respectivebranch lines and the voltages at the nodes can be measured by suitablemeters connected to all of the branch lines and nodes. That is, eachbranch line has an ammeter 50 connected serially therein, and voltmeters52 connected between the respective nodes and ground. For example, oneeach of said ammeters and voltmeters are shown in FIG. 5. The measuredvalues of the currents and voltages are multiplied by respective ratesof conversion by the measuring devices, predetermined on the basis ofthe correspondence of parameters between the actual electric powersystem and the simulated resistance network as previously described tocomplete the computation of the requisite power flow. That is, therequisite reactive power Q and voltage V are determined by theresistance network of FIG. 4 while the requisite active power and phaseangle are determined by the arrangement of FIG. 5. The computation of Pand 6 in FIG. 5, and the computation'of Q and AV in FIGS. 4 arepermitted by changing the energization state of transfer relay 16 inFIGS. 2 and 3.

It will be appreciated that the result of the computation and known lineresistances of the power system may be used in equations (5) and (6) inorder to increase the accuracy of computation.

What we claim is:

l. A simulated power system for use in computing power flow in an actualpower system, said simulated power system comprising resistance networkmeans including a plurality of resistors connected respectively betweena plurality of pairs of terminals which define a plurality of nodes ofsaid network, said network means corresponding to a transmission systemof said actual power system, simulated power means for supplying powerto said network means and including a separate simulated power sourcefor each power source of the actual system, each of said simulated powersource being coupled to a respective node to apply a voltage to saidnode, simulated load means for simulating loading characteristics ofsaid actual system and including a separate constant current generatormeans for each load of the actual system, each said constant currentgenerator means being coupled to a respective node for drawing currenttherefrom, current meter means connected to said network means formeasuring current levels through each one of said resistors and voltagemeter means for measuring levels at each of said nodes, said simulatedpower source and load means to simulate the actual system in accordancewith the equations where Pmn is the active power through one saidresistor connected between selected nodes m and n, Qmn is the reactivepower through said one resistor, 6m, 0n are the phase angles at theselected nodes m and n, AVm, AVn are the differences between actualvoltages and standard voltages at the selected nodes m and n, i,,,,, isthe current through the branch between the selected nodes m and n asmeasured by said meter means, r,,,,, is the resistance value of said oneresistor, and v,,, and v are the voltages at the selected nodes m and nas measured by said meter means, wherein active power Pmn corresponds tosaid current i,,,,,, and phase angles 0m and On correspond to voltagesv,,, and v,, in the case of computing active power and phase angle; andwherein reactive power Qmn corresponds to current i,,,,,, and differencevoltages AVm and AVn correspond to voltage v,, and v,, in the case ofcomputing reactive power and difference voltage.

2. A simulated power system as set forth in claim 1, in which saidsimulated power source includes a DC potential source, a potentiometerhaving an adjustable tap, and having end leads connected across saidpotential source, an operational amplifier having first and secondinputs and having an output, said first input being connected to saidtap, a feedback resistor having a first terminal connected to saidoperational amplifier output and a second terminal coupled to arespective one of said respective power source nodes, and an invertercircuit coupled between said second terminal of said feedback resistorand said second input of said operational amplifier, whereby a constantcurrent source is provided at said second terminal of said feedbackresistor, said constant current being variable with a variation ofposition of said tap.

3. A simulated power system as set forth in claim 2, further comprisingswitching means connected to said feedback resistor and said invertercircuit, and means for operating said switching means to an actuatedposition to disconnect said inverter circuit from its said circuitconnection with said operational amplifier, and to provide a shortcircuit across said feedback resistor, whereby a constant voltage isprovided at said second terminal of said feedback resistor uponoperation of said switch means to said actuated position.

4. A simulated power system as set forth in claim 2, in which saidpotentiometer has a grounded center-tap, wherein said adjustable tap ispositionable to apply selectively a negative or

1. A simulated power system for use in computing power flow in an actualpower system, said simulated power system comprising resistance networkmeans including a plurality of resistors connected respectively betweena plurality of pairs of terminals which define a plurality of nodes ofsaid network, said network means corresponding to a transmission systemof said actual power system, simulated power means for supplying powerto said network means and including a separate simulated power sourcefor each power source of the actual system, each of said simulated powersource being coupled to a respective node to apply a voltage to saidnode, simulated load means for simulating loading characteristics ofsaid actual system and including a separate constant current generatormeans for each load of the actual system, each said constant currentgenerator means being coupled to a respective node for drawing currenttherefrom, current meter means connected to said network means formeasuring current levels through each one of said resistors and voltagemeter means for measuring levels at each of said nodes, said simulatedpower source and load means to simulate the actual system in accordancewith the equations
 2. A simulated power system as set forth in claim 1,in which said simulated power source includes a DC potential source, apotentiometer having an adjustable tap, and having end leads connectedacross said potential source, an operational amplifier having first andsecond inputs and having an output, said first input being connected tosaid tap, a feedback resistor having a first terminal connected to saidoperational amplifier output and a second terminal coupled to arespective one of said respective power source nodes, and an invertercircuit coupled between said second terminal of said feedback resistorand said second input of said operational amplifier, whereby a constantcurrent source is provided at said second terminal of said feedbackresistor, said constant current being variable with a variation ofposition of said tap.
 3. A simulated power system as set forth in claim2, further comprising switching means connected to said feedbackresistor and said inverter circuit, and means for operating saidswitching means to an actuated position to disconnect said invertercircuit from its said circuit connection with said operationalamplifier, and to provide a short circuit across said feedback resistor,whereby a constant voltage is provided at said second terminal of saidfeedback resistor upon operation of said switch means to said actuatedposition.
 4. A simulated power system as set forth in claim 2, in whichsaid potentiometer has a grounded center-tap, wherein said adjustabletap is positionable to apply selectively a negative or positive voltageto said first input of said operational amplifier, whereby said secondterminal of said feedback resistor provides selectively a constantcurrent source or a constant current drain for use respectively as asaid simulated power source or a said simulated load.